MathNet 2019-part-03 — 184 problems (EN–VI) Question 144

Let $ABC$ be an acute-angled triangle. Let $D$ be the foot of the internal bisector from $A$ and $M$ the midpoint of $AD$. Moreover, let $X$ be a point on segment $BM$ such that $\angle MXA = \angle DAC$.
Prove that $AX$ is perpendicular to $XC$.